Stochastic claims reserving methods in insurance

Medientyp: E-Book

Titel: Stochastic claims reserving methods in insurance

Enthält: Stochastic Claims Reserving Methods in Insurance; Contents; Preface; Acknowledgement; 1 Introduction and Notation; 1.1 Claims process; 1.1.1 Accounting principles and accident years; 1.1.2 Inflation; 1.2 Structural framework to the claims-reserving problem; 1.2.1 Fundamental properties of the claims reserving process; 1.2.2 Known and unknown claims; 1.3 Outstanding loss liabilities, classical notation; 1.4 General remarks; 2 Basic Methods; 2.1 Chain-ladder method (distribution-free); 2.2 Bornhuetter-Ferguson method; 2.3 Number of IBNyR claims, Poisson model
2.4 Poisson derivation of the CL algorithm3 Chain-Ladder Models; 3.1 Mean square error of prediction; 3.2 Chain-ladder method; 3.2.1 Mack model (distribution-free CL model); 3.2.2 Conditional process variance; 3.2.3 Estimation error for single accident years; 3.2.4 Conditional MSEP, aggregated accident years; 3.3 Bounds in the unconditional approach; 3.3.1 Results and interpretation; 3.3.2 Aggregation of accident years; 3.3.3 Proof of Theorems 3.17, 3.18 and 3.20; 3.4 Analysis of error terms in the CL method; 3.4.1 Classical CL model; 3.4.2 Enhanced CL model; 3.4.3 Interpretation
3.4.4 CL estimator in the enhanced model3.4.5 Conditional process and parameter prediction errors; 3.4.6 CL factors and parameter estimation error; 3.4.7 Parameter estimation; 4 Bayesian Models; 4.1 Benktander-Hovinen method and Cape-Cod model; 4.1.1 Benktander-Hovinen method; 4.1.2 Cape-Cod model; 4.2 Credible claims reserving methods; 4.2.1 Minimizing quadratic loss functions; 4.2.2 Distributional examples to credible claims reserving; 4.2.3 Log-normal/Log-normal model; 4.3 Exact Bayesian models; 4.3.1 Overdispersed Poisson model with gamma prior distribution
4.3.2 Exponential dispersion family with its associated conjugates4.4 Markov chain Monte Carlo methods; 4.5 Bühlmann-Straub credibility model; 4.6 Multidimensional credibility models; 4.6.1 Hachemeister regression model; 4.6.2 Other credibility models; 4.7 Kalman filter; 5 Distributional Models; 5.1 Log-normal model for cumulative claims; 5.1.1 Known variances 2j; 5.1.2 Unknown variances; 5.2 Incremental claims; 5.2.1 (Overdispersed) Poisson model; 5.2.2 Negative-Binomial model; 5.2.3 Log-normal model for incremental claims; 5.2.4 Gamma model; 5.2.5 Tweedie's compound Poisson model
5.2.6 Wright's model6 Generalized Linear Models; 6.1 Maximum likelihood estimators; 6.2 Generalized linear models framework; 6.3 Exponential dispersion family; 6.4 Parameter estimation in the EDF; 6.4.1 MLE for the EDF; 6.4.2 Fisher's scoring method; 6.4.3 Mean square error of prediction; 6.5 Other GLM models; 6.6 Bornhuetter-Ferguson method, revisited; 6.6.1 MSEP in the BF method, single accident year; 6.6.2 MSEP in the BF method, aggregated accident years; 7 Bootstrap Methods; 7.1 Introduction; 7.1.1 Efron's non-parametric bootstrap; 7.1.2 Parametric bootstrap
7.2 Log-normal model for cumulative sizes

Beteiligte: Wüthrich, Mario V. [VerfasserIn]; Merz, Michael [VerfasserIn]

Erschienen: Chichester, England; Hoboken, NJ: John Wiley & Sons, 2008
Online-Ausg., [S.l.]: eblib

Umfang: XII, 424 S.; graph. Darst

Sprache: Englisch

ISBN: 9780470723463; 0470723467

RVK-Notation: SK 980 : Wirtschaftsmathematik, Ökonometrie, Produktionstheorie
QQ 630 : Rechnungswesen: Buchführung, Bilanz; Versicherungsmathematik etc.
QH 300 : Allgemeines

Schlagwörter: Versicherungsbetrieb > Schadenrückstellung > Mathematisches Modell > Stochastik
Versicherungsbetrieb > Schadenrückstellung > Mathematisches Modell > Stochastik > Online-Ressource

Art der Reproduktion: Online-Ausg.

Hersteller der Reproduktion: [S.l.]: eblib

Entstehung:

Anmerkungen: Includes bibliographical references and index

Beschreibung: "It is astonishing that the methods used for claims reserving in non life-insurance are, even still today, driven by a deterministic understanding of one or several computational algorithms. Stochastic Claims Reserving Methods in Insurance is tremendously widening this traditional understanding. In this text reserving is model driven, computational algorithms become a consequence of the chosen model. Only with this approach it makes sense to ask how predicted reserves might vary. Stochastic reserving is hence the corner stone of successful risk management for the technical result of an insurance company. Mario Wüthrich and Michael Merz have to be congratulated for opening the eyes of the non-life-actuary to a new and modern dimension." -Hans Bühlmann, Swiss Federal Institute of Technology, Zurich "Assessing the best estimate of insurance liabilities and modelling their adverse developments are among the new frontiers of insurance under the new IAS and the proposed new solvency regimes. This book makes a leap towards these frontiers. The variegated issue of predicting outstanding loss liabilities in non-life insurance is addressed using the unified framework of theory of stochastic processes. The proposed approach provides valuable tools for tackling one of the most challenging forecasting problems in insurance." -Franco Moriconi, Professor of Finance, University of Perugia.

Stochastic Claims Reserving Methods in Insurance -- Contents -- Preface -- Acknowledgement -- 1 Introduction and Notation -- 1.1 Claims process -- 1.1.1 Accounting principles and accident years -- 1.1.2 Inflation -- 1.2 Structural framework to the claims-reserving problem -- 1.2.1 Fundamental properties of the claims reserving process -- 1.2.2 Known and unknown claims -- 1.3 Outstanding loss liabilities, classical notation -- 1.4 General remarks -- 2 Basic Methods -- 2.1 Chain-ladder method (distribution-free) -- 2.2 Bornhuetter-Ferguson method -- 2.3 Number of IBNyR claims, Poisson model -- 2.4 Poisson derivation of the CL algorithm -- 3 Chain-Ladder Models -- 3.1 Mean square error of prediction -- 3.2 Chain-ladder method -- 3.2.1 Mack model (distribution-free CL model) -- 3.2.2 Conditional process variance -- 3.2.3 Estimation error for single accident years -- 3.2.4 Conditional MSEP, aggregated accident years -- 3.3 Bounds in the unconditional approach -- 3.3.1 Results and interpretation -- 3.3.2 Aggregation of accident years -- 3.3.3 Proof of Theorems 3.17, 3.18 and 3.20 -- 3.4 Analysis of error terms in the CL method -- 3.4.1 Classical CL model -- 3.4.2 Enhanced CL model -- 3.4.3 Interpretation -- 3.4.4 CL estimator in the enhanced model -- 3.4.5 Conditional process and parameter prediction errors -- 3.4.6 CL factors and parameter estimation error -- 3.4.7 Parameter estimation -- 4 Bayesian Models -- 4.1 Benktander-Hovinen method and Cape-Cod model -- 4.1.1 Benktander-Hovinen method -- 4.1.2 Cape-Cod model -- 4.2 Credible claims reserving methods -- 4.2.1 Minimizing quadratic loss functions -- 4.2.2 Distributional examples to credible claims reserving -- 4.2.3 Log-normal/Log-normal model -- 4.3 Exact Bayesian models -- 4.3.1 Overdispersed Poisson model with gamma prior distribution.

Nur in Feld suchen:

Zuletzt gesuchte Begriffe: